CR circuit: harmonic response

Control theory

In this article, we will deal with a simple high pass filter, made using a capacitor and a resistor, connected in series. We already saw something similar in the article about a RC circuit, but this time the output voltage will be measured on the resistor instead of the capacitor. Obviously the circuit will behave in a completely different way. For the sake of simplicity, the calculations will be carried out in the Laplace domain.

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Using the voltage divider formula, we can write:


Simplifying the fraction and dividing by V_i, we can write:


We can now identify the parameters in the transfer function. From the formula above we can easily see that there is a binomial factor in the denominator. In the numerator we can identify a zero in the origin and two constants, R and C that will be part of the static gain K. As usual these values refer to the Bode form formula, reported below.


As a result we will choose the folowing parameters.

Parameter Value
n -1
\tau_1 Time constant in the denumerator. There is just one: RC